Re: (*) -> 1

[Óscar Fuentes]

Michael Heerdegen <michael_heerdegen@web.de> writes:

> Óscar Fuentes <ofv@wanadoo.es> writes:
>
>> The languages that use the concept of partially applied function usually
>> have no support for variadic functions, so the duality problem you refer
>> to is not an issue.
>
> Interesting.  I do not know many other languages.
>
> I see your point now: while I wrote about the procedure of finding an
> interpretation [of the technical or mathematical semantics of a formula]
> in the real world [this is what had been ongoing: Ferraris etc], you
> mention that even the technical/theoretical semantics of a formula like
> (*) can be different.  This is an interesting point, especially since
> terms like "right" and "wrong" had been used.
>
> Although I think the "meaning" of the expression (*) in Elisp is clear,
> it describes a mathematical term, so the question, asked specifically
> for Elisp, has to be answered using the mathematical background.  In my
> understanding the OP asked specifically about the empty algebraic
> product.

I was prompted to enter the discussion when I saw your reference to
Mathematics. As almost every other math-related thing in computers,
Elisp's + is a toy representation of Sigma. And then the relevant
characteristics of Sigma for this discussion are a convention among
practitioners, not a proper mathematical fact.

Although it is possible that the implementors were inspired by Sigma, I
think it is more probable that they made + variadic because s-exps like
(+ (+ 1 2) 3) are awkward and then extended the function with support
for 0 and 1 arguments because they are convenient when defining macros.